Non-square blind source separation under coherent noise by beamforming and timefrequency masking

To be applicable in realistic scenarios, blind source sep-aration approaches should deal evenly with non-square cases and the presence of noise. We consider an additive noise mixing model with an arbitrary number of sensors and pos-sibly more sources than sensors (the non-square case) when sources are disjointly orthogonal. We formulate the max-imum likelihood estimation of the coherent noise model, suitable when sensors are nearby and the noise field is close to isotropic, and also under the direct-path far-field assump-tions. The implementation of the derived criterion involves iterating two steps: a partitioning of the time-frequency plane for separation followed by an optimization of the mixing pa-rameter estimates. The structure of the solution is surprising at first but logical: it consists of a beamforming linear filter, which reduces noise, and a filter across time-frequency do-main to separate sources. The solution is applicable to an arbitrary number of microphones and sources. Experimen-tally, we show the capability of the technique to separate four voices from two, four, six, and eight channel record-ings in the presence of isotropic noise. 1 1